MULTIPLE CHOICE. (3 Points Each) Choose the one alternative that best completes the statement or answers the question. 1) When an opinion poll says that "with 95% confidence" the margin of error for its results is plus or minus 3 percentage points, this means that 1) _______ A) the percentage of people who said "Yes" to the question was between 92% and 98%. B) between 92% and 98% of the people chosen for the sample were contacted. C) we can be certain that the true population value is within 3 points of the sample result. D) 95% of all samples chosen in the same way as this one give results within 3 points of the true population value. 2) For a fixed level of confidence, such as 95%, what effect does increasing the sample size have on the resulting confidence interval? 2) _______ A) The interval is the same width as before. B) The interval is now narrower. C) The interval is now wider. D) We cannot tell from the given information. 3) An advantage of a 99% confidence interval over a 95% confidence interval is 3) _______ A) the method used to construct the interval, when used over and over, produces intervals which include the true population proportion more often. B) the margin of error is smaller. C) the width of the interval is smaller. D) the width of the interval is larger. 4) A company supervisor wants to estimate the mean length of time it takes employees to install mufflers on new cars. It is believed from previous studies that the population standard deviation is 5.03 minutes. How large a sample is required to be 95% confident and to have a maximum margin of error of 1.35? 4) _______ A) 7 B) 8 C) 53 D) 54 5) A survey of 250 homeless persons showed that 37 were veterans. Find a point estimate p, for the population proportion of homeless persons who are veterans. 5) _______ A) 0.148 B) 0.129 C) 0.174 D) 0.852 6) A random sample of 40 college students has a mean earnings of $3120 with a standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. 6) _______ A) Use a t-distribution. B) Use a normal distribution. C) Neither a normal distribution nor a t-distribution can be used. 7) For a sample of 20 IQ scores the mean score is 105.8. The distribution of IQ scores is known to be approximately normal, and the sample standard deviation, s, is 15. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. 7) _______ A) Use a t-distribution. B) Use a normal distribution. C) Neither a normal distribution nor a t-distribution can be used. 8) A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $30.25. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of prices is skewed to the left. 8) _______ A) Use a normal distribution. B) Use a t-distribution. C) Neither a normal distribution nor a t-distribution can be used. 9) Find the value of E, the margin of error, for c = 0. 90, n = 10 and s = 3.7. 9) _______ A) 0.68 B) 1.62 C) 2.14 D) 2.12 10) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches. 10) ______ A) 0.0188 B) 0.2119 C) 0.9811 D) 0.3071 11) A Gallup Poll showed that 60% of Americans believe in hell. (The question was, "Do you believe there is a place where those who led bad lives and died without repentance are eternally damned?") The poll contacted 1,108 adults by telephone. The margin of error was ±4 percentage points. For this situation, a margin of error of ± 4 percentage points means that 11) ______ A) only four percent of those surveyed failed to respond. B) four percent of the population may change their minds. C) it would be unlikely to have seen the 60% if the parameter were not between 56% and 64%. D) there is a 96% chance that the statistic calculated will be the same as the parameter of interest. 12) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests and scores 860 on the SAT and 16 on the ACT. Compare the scores. 12) ______ A) A score of 860 on the SAT test was better. B) You cannot determine which score is better from the given information. C) The two scores are statistically the same. D) A score of 16 on the ACT test was better. 13) Find the z-score that is less than the mean and for which about 70% of the distribution's area lies to its right. 13) ______ A) -0.53 B) -0.47 C) -0.98 D) -0.81 14) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of 1.96. 14) ______ A) 129.4 B) 132.1 C) 115.6 D) 122.4 15) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 120. Find the z-score corresponding to this value. 15) ______ A) 1.33 B) -0.67 C) -1.33 D) 0.67 16) Find the area under the standard normal curve between z = 1 and z = 2. 16) ______ A) 0.8413 B) 0.2139 C) 0.5398 D) 0.1359 17) Find the area under the standard normal curve to the left of z = 1.25. 17) ______ A) 0.8944 B) 0.2318 C) 0.1056 D) 0.7682 18) Find the area of the indicated region under the standard normal curve. 18) ______ A) 0.9177 B) 0.0968 C) 0.0823 D) 0.9032 19) A question has five multiple-choice answers. Find the probability of guessing an incorrect answer. 19) ______ A) B) C) D) 20) State whether the variable is discrete or continuous. The cost of a Statistics textbook 20) ______ A) discrete B) continuous 21) State whether the variable is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska 21) ______ A) discrete B) continuous 22) Determine the probability distribution's missing value. The probability that a tutor will see 0, 1, 2, 3, or 4 students 22) ______ A) 0.24 B) 0.76 C) 0.95 D) - 0.29 23) One thousand tickets are sold at $1 each. One ticket will be randomly selected and the winner will receive a computer valued at $1200. What is the expected value if a person buys one ticket? 23) ______ A) -$0.20 B) $1.00 C) $0.20 D) -$1.00 Use the following information to answer the next two questions: A recent Gallup Poll interviewed a random sample of 1,523 adults. Of these, 868 bought a lottery ticket in the past year. 24) In which of the following cases would the confidence interval be wider than a 95% confidence interval? 24) ______ A) If the sample size were 2,100 instead of 1,523. B) If the confidence level were 98% instead of 95%. C) If the population size were smaller. D) If the confidence level were 92% instead of 95%. 25) Suppose that in fact (unknown to Gallup) exactly 60% of all adults bought a lottery ticket in the past year. If Gallup took many SRSs of 1523 people, the sample proportion who bought a ticket would vary from sample to sample. The sampling distribution would be close to normal with 25) ______ A) a mean of 0.6 and a standard deviation of .0127. B) a mean of 0.57 and a standard deviation of .0127. C) a mean of 0.57 and a standard deviation of .00016. D) a mean of 0.6 and a standard deviation of .00016. SHORT ANSWER. (4 Points Each) Write your answer in the space provided. 26) Identify the sample space of the probability experiment: recording the day of the week on which a person was born. 27) Find the critical value corresponds to a 92% confidence level. that 28) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 25 adults are randomly selected, find the probability that their mean body temperature is less than 99° F. 29) Find the z-score that corresponds to the given area under the standard normal curve. CONFIDENCE INTERVALS. (5 Points Each) Write your answer in the space provided. 30) A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 95% confidence interval for the true mean. Assume that the account balances are normally distributed. 31) In a random sample of 60 computers, the mean repair cost was $150 with a standard deviation of $36. a) Construct the 99% confidence interval for the population mean repair cost. b) If the level of confidence was lowered to 90%, what will be the effect on the confidence interval? 32) The USA Today claims that 44% of adults who access the Internet read the international news online. You want to check the accuracy of their claim by surveying a random sample of 120 adults who access the Internet and asking them if they read the international news online. Fifty-two adults responded "yes." Use a 95% confidence interval to test the newspaper's claim. 1) D 2) B 3) A 4) D 5) A 6) B 7) A 8) C 9) C 10) C 11) C 12) A 13) A 14) A 15) A 16) D 17) A 18) D 19) B 20) A 21) B 22) A 23) C 24) B 25) A 26) (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday) 27) 1.75 28) 0.9996 29) z = 3.07 31) a) ($138, $162) b) A decrease in the level of confidence will decrease the width of the confidence interval. 32) (0.344, 0.522) Because the interval contains the reported percentage of 44%, the newspaper's claim is accurate.
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